System of generalized $H$-resolvent equations and the corresponding system of generalized variational inclusions

Abstract

The aim of this paper is to introduce a new system of generalized H- resolvent equations in uniformly smooth Banach spaces and to men- tion the corresponding system of variational inclusions. An equivalence relation is established between the system of generalized H-resolvent equations and the system of variational inclusions. We also prove the existence of solutions for the system of generalized H-resolvent equa- tions and the convergence of the iterative sequences generated by the algorithm. Our results are new and generalize many known results appearing in the literature.